16,914 research outputs found
An alternative non-Markovianity measure by divisibility of dynamical map
Identifying non-Markovianity with non-divisibility, we propose a measure for
non-Markovinity of quantum process. Three examples are presented to illustrate
the non-Markovianity, measure for non-Markovianity is calculated and discussed.
Comparison with other measures of non-Markovianity is made. Our
non-Markovianity measure has the merit that no optimization procedure is
required and it is finite for any quantum process, which greatly enhances the
practical relevance of the proposed measure.Comment: 6 pages, 3 figue
Effective Hamiltonian Approach to the Master Equation
A method of exactly solving the master equation is presented in this letter.
The explicit form of the solution is determined by the time evolution of a
composite system including an auxiliary system and the open system in question.
The effective Hamiltonian governing the time evolution of the composed system
are derived from the master equation. Two examples, the dissipative two-level
system and the damped harmonic oscillator, are presented to illustrate the
solving procedure.
PACS number(s): 05.30.-d, 05.40.+j, 42.50.CtComment: 4 pages, no figure
Modeling Bitcoin Contracts by Timed Automata
Bitcoin is a peer-to-peer cryptographic currency system. Since its
introduction in 2008, Bitcoin has gained noticeable popularity, mostly due to
its following properties: (1) the transaction fees are very low, and (2) it is
not controlled by any central authority, which in particular means that nobody
can "print" the money to generate inflation. Moreover, the transaction syntax
allows to create the so-called contracts, where a number of
mutually-distrusting parties engage in a protocol to jointly perform some
financial task, and the fairness of this process is guaranteed by the
properties of Bitcoin. Although the Bitcoin contracts have several potential
applications in the digital economy, so far they have not been widely used in
real life. This is partly due to the fact that they are cumbersome to create
and analyze, and hence risky to use.
In this paper we propose to remedy this problem by using the methods
originally developed for the computer-aided analysis for hardware and software
systems, in particular those based on the timed automata. More concretely, we
propose a framework for modeling the Bitcoin contracts using the timed automata
in the UPPAAL model checker. Our method is general and can be used to model
several contracts. As a proof-of-concept we use this framework to model some of
the Bitcoin contracts from our recent previous work. We then automatically
verify their security in UPPAAL, finding (and correcting) some subtle errors
that were difficult to spot by the manual analysis. We hope that our work can
draw the attention of the researchers working on formal modeling to the problem
of the Bitcoin contract verification, and spark off more research on this
topic
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